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URL: https://oeis.org/A091598

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A091598
Triangle read by rows: T(n,0) = A078008(n), T(n,m) = T(n-1,m-1) + T(n-1,m).
1
1, 0, 1, 2, 1, 1, 2, 3, 2, 1, 6, 5, 5, 3, 1, 10, 11, 10, 8, 4, 1, 22, 21, 21, 18, 12, 5, 1, 42, 43, 42, 39, 30, 17, 6, 1, 86, 85, 85, 81, 69, 47, 23, 7, 1, 170, 171, 170, 166, 150, 116, 70, 30, 8, 1, 342, 341, 341, 336, 316, 266, 186, 100, 38, 9, 1, 682, 683, 682, 677, 652, 582, 452, 286, 138, 47, 10, 1
OFFSET
0,4
COMMENTS
A Jacobsthal-Pascal triangle.
FORMULA
k-th column has e.g.f. ((1-x)/(1-x-x^2))*(x/(1-x))^k.
EXAMPLE
Triangle starts as:
1;
0, 1;
2, 1, 1;
2, 3, 2, 1;
6, 5, 5, 3, 1;
10, 11, 10, 8, 4, 1;
22, 21, 21, 18, 12, 5, 1;
42, 43, 42, 39, 30, 17, 6, 1; ...
MATHEMATICA
T[n_, k_]:= If[k==0, (2^n + 2*(-1)^n)/3, If[k<0 || k>n, 0, T[n-1, k-1] + T[n-1, k]]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 04 2019 *)
PROG
(PARI) {T(n, k) = if(k==0, (2^n + 2*(-1)^n)/3, if(k<0 || k>n, 0, T(n-1, k-1) + T(n-1, k)))}; \\ G. C. Greubel, Jun 04 2019
(SageMath)
def T(n, k):
if (k<0 or k>n): return 0
elif (k==0): return (2^n + 2*(-1)^n)/3
else: return T(n-1, k-1) + T(n-1, k)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Jun 04 2019
CROSSREFS
Columns include A078008, A001045, A000975, A011377. Row sums give A084219.
Cf. A091597.
Sequence in context: A238348 A143066 A338198 * A144021 A334591 A177962
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jan 23 2004
STATUS
approved