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URL: https://oeis.org/A176242

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A176242
Triangle read by rows, T(n, 1) = 1 and T(n,k) = q^k*T(n-1, k) + T(n-1, k-1) for 2 <= k <= n, n >= 1, with q=2.
3
1, 1, 1, 1, 5, 1, 1, 21, 13, 1, 1, 85, 125, 29, 1, 1, 341, 1085, 589, 61, 1, 1, 1365, 9021, 10509, 2541, 125, 1, 1, 5461, 73533, 177165, 91821, 10541, 253, 1, 1, 21845, 593725, 2908173, 3115437, 766445, 42925, 509, 1, 1, 87381, 4771645, 47124493, 102602157, 52167917, 6260845, 173229, 1021, 1
OFFSET
1,5
COMMENTS
Row sums are: {1, 2, 7, 36, 241, 2078, 23563, 358776, 7449061, 213188690, ...}.
REFERENCES
Steve Roman, The Umbral Calculus, Dover Publications, New York (1984), page 176
FORMULA
T(n,k) = T(n-1, k-1) + q^k*T(n-1, k), with q=2.
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 5, 1;
1, 21, 13, 1;
1, 85, 125, 29, 1;
1, 341, 1085, 589, 61, 1;
1, 1365, 9021, 10509, 2541, 125, 1;
1, 5461, 73533, 177165, 91821, 10541, 253, 1;
1, 21845, 593725, 2908173, 3115437, 766445, 42925, 509, 1;
MAPLE
T:= proc(n, k) option remember;
q:=2;
if k=1 or k=n then 1
else T(n-1, k-1) + q^k*T(n-1, k)
fi; end:
seq(seq(T(n, k), k=1..n), n=1..12); # G. C. Greubel, Nov 22 2019
MATHEMATICA
q:=2; T[n_, k_]:= T[n, k]= If[k==1 || k==n, 1, q^k*T[n-1, k] + T[n-1, k-1]]; Table[T[n, k], {n, 12}, {k, n}]//Flatten (* modified by G. C. Greubel, Nov 22 2019 *)
PROG
(PARI) T(n, k) = my(q=2); if(k==1 || k==n, 1, q^k*T(n-1, k) + T(n-1, k-1)); \\ G. C. Greubel, Nov 22 2019
(Magma)
function T(n, k)
q:=2;
if k eq 1 or k eq n then return 1;
else return T(n-1, k-1) + q^k*T(n-1, k);
end if; return T; end function;
[T(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Nov 22 2019
(SageMath)
@CachedFunction
def T(n, k):
q=2;
if (k==1 or k==n): return 1
else: return q^k*T(n-1, k) + T(n-1, k-1)
[[T(n, k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Nov 22 2019
CROSSREFS
Cf. this sequence (q=2), A176243 (q=3), A176244 (q=4).
Sequence in context: A047909 A171243 A111577 * A036969 A080249 A333143
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Apr 12 2010
EXTENSIONS
Edited by G. C. Greubel, Nov 22 2019
Definition clarified by Georg Fischer, Nov 12 2021
STATUS
approved