A235537 Expansion of (6 + 13*x - 8*x^2 - 8*x^3 + 6*x^4)/((1 + x)^2*(1 - x)^3).

6, 19, 23, 41, 49, 72, 84, 112, 128, 161, 181, 219, 243, 286, 314, 362, 394, 447, 483, 541, 581, 644, 688, 756, 804, 877, 929, 1007, 1063, 1146, 1206, 1294, 1358, 1451, 1519, 1617, 1689, 1792, 1868, 1976, 2056, 2169, 2253, 2371, 2459, 2582, 2674, 2802, 2898

Offset

0,1

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Bruno Berselli, Triangular spiral which contains the terms of A235537 (see A051682).

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Formula

G.f.: (6 + 13*x - 8*x^2 - 8*x^3 + 6*x^4)/((1 + x)^2*(1 - x)^3).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

a(n) = (6*n*(3*n + 17) - (2*n + 43)*(-1)^n + 11)/16 + 8. The terms a(2k) are in A235332; the closed form of the terms a(2k+1) is n*(9*n+35)/2+19.

Mathematica

Table[(6 n (3 n + 17) - (2 n + 43) (-1)^n + 11)/16 + 8, {n, 0, 50}]
LinearRecurrence[{1, 2, -2, -1, 1}, {6, 19, 23, 41, 49}, 80] (* Harvey P. Dale, Aug 22 2015 *)

Prog

(Magma) [(6*n*(3*n+17)-(2*n+43)*(-1)^n+11)/16+8: n in [0..50]];

Crossrefs

Cf. A235332.

Sequence in context: A012589 A009048 A294313 * A046955 A042215 A041911

Adjacent sequences: A235534 A235535 A235536 * A235538 A235539 A235540

Keyword

nonn,easy

Author

Bruno Berselli, Jan 23 2014

Status

approved