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URL: https://oeis.org/A048507

⇱ A048507 - OEIS

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A048507
a(n) = T(2,n), array T given by A048505.
3
1, 10, 35, 101, 269, 685, 1693, 4093, 9725, 22781, 52733, 120829, 274429, 618493, 1384445, 3080189, 6815741, 15007741, 32899069, 71827453, 156237821, 338690045, 731906045, 1577058301, 3388997629, 7264534525, 15535702013, 33151778813, 70598524925, 150055419901
OFFSET
0,2
COMMENTS
n-th difference of a(n), a(n-1), ..., a(0) is (9, 16, 25, 36, 49, ...).
FORMULA
a(n) = (n^2+9*n+16)*2^(n-2) - 3. - Ralf Stephan, Feb 05 2004
From Colin Barker, Nov 27 2014: (Start)
a(n) = 7*a(n-1) - 18*a(n-2) + 20*a(n-3) - 8*a(n-4).
G.f.: (16*x^3-17*x^2+3*x+1)/((x-1)*(2*x-1)^3). (End)
E.g.f.: exp(x)*(exp(x)*(4 + 5*x + x^2) - 3). - Elmo R. Oliveira, Oct 27 2025
MATHEMATICA
LinearRecurrence[{7, -18, 20, -8}, {1, 10, 35, 101}, 30] (* Harvey P. Dale, Jan 21 2021 *)
PROG
(Magma) [(n^2+9*n+16) * 2^(n-2) - 3: n in [0..30]]; // Vincenzo Librandi, Sep 26 2011
(PARI) Vec((16*x^3-17*x^2+3*x+1)/((x-1)*(2*x-1)^3) + O(x^100)) \\ Colin Barker, Nov 27 2014
CROSSREFS
Cf. A048505.
Sequence in context: A358248 A309883 A049736 * A240267 A359317 A221907
KEYWORD
nonn,easy
STATUS
approved