A272129 a(n) = 32*n^2 - 56*n + 25.

25, 1, 41, 145, 313, 545, 841, 1201, 1625, 2113, 2665, 3281, 3961, 4705, 5513, 6385, 7321, 8321, 9385, 10513, 11705, 12961, 14281, 15665, 17113, 18625, 20201, 21841, 23545, 25313, 27145, 29041, 31001, 33025, 35113, 37265, 39481, 41761, 44105, 46513, 48985

Offset

0,1

Comments

Subsequence of A001844.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014 (page 16).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

O.g.f.: (25 - 74*x + 113*x^2)/(1-x)^3.

E.g.f.: (25 - 24*x + 32*x^2)*exp(x).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

n*a(n) = 1 + 3^5*(n-1)/(n+1) + 5^5*((n-1)*(n-2))/((n+1)*(n+2)) + ... for n >= 1. See A245244. - Peter Bala, Jan 19 2019

Maple

[32*n^2-56*n+25$n=0..40]; # Muniru A Asiru, Jan 28 2019

Mathematica

Table[32 n^2 - 56 n + 25, {n, 0, 40}]
LinearRecurrence[{3, -3, 1}, {25, 1, 41}, 50] (* Harvey P. Dale, Jul 03 2018 *)

Prog

(Magma) [32*n^2 - 56*n + 25: n in [0..50]];
(PARI) lista(nn) = for(n=0, nn, print1(32*n^2-56*n+25, ", ")); \\ Altug Alkan, Apr 26 2016

Crossrefs

Cf. A001844, A272126, A272127, A272128, A272131, A272132, A272133, A245244.

Sequence in context: A377611 A126647 A040648 * A232989 A040649 A104707

Adjacent sequences: A272126 A272127 A272128 * A272130 A272131 A272132

Keyword

nonn,easy

Author

Vincenzo Librandi, Apr 26 2016

Status

approved