A264754 Expansion of (1 + 2*x - 2*x^3 + x^4)/((1 - x)^3*(1 + x)^2).

1, 3, 5, 7, 11, 13, 19, 21, 29, 31, 41, 43, 55, 57, 71, 73, 89, 91, 109, 111, 131, 133, 155, 157, 181, 183, 209, 211, 239, 241, 271, 273, 305, 307, 341, 343, 379, 381, 419, 421, 461, 463, 505, 507, 551, 553, 599, 601, 649, 651, 701, 703, 755, 757, 811, 813, 869, 871, 929, 931, 991, 993, 1055, 1057, 1121, 1123

Offset

0,2

Comments

Interleaving of A002061 and A028387.

All members are odd.

Primes in this sequence: 3, 5, 7, 11, 13, 19, 29, 31, 41, 43, 71, 73, 89, 109, 131, 157, 181, 211, 239, 241, 271, 307, 379, 419, 421, 461, 463, 599, 601, 701, 757, 811, 929, 991, ...

Links

Carauleanu Marc, Table of n, a(n) for n = 0..2222

Ilya Gutkovskiy, Illustration

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

Formula

O.g.f.: (1 + 2*x - 2*x^3 + x^4)/((1 - x)^3*(1 + x)^2).

E.g.f.: ((-3 - 2*x)*exp(-x) + (11 + 12*x + 2*x^2)*exp(x))/8

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

a(n) = (2*n*(n + (-1)^n + 5) - 3*(-1)^n + 11)/8.

Mathematica

LinearRecurrence[{1, 2, -2, -1, 1}, {1, 3, 5, 7, 11}, 66]
Table[(2 n (n + (-1)^n + 5) - 3 (-1)^n + 11)/8, {n, 0, 65}]

Prog

(PARI) Vec((1+2*x-2*x^3+x^4)/((1-x)^3*(1+x)^2) + O(x^99)) \\ Altug Alkan, Aug 27 2016

Crossrefs

Cf. A002061, A005408, A028387, A055802.

Sequence in context: A026603 A287437 A126991 * A130289 A071329 A109358

Adjacent sequences: A264751 A264752 A264753 * A264755 A264756 A264757

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Aug 27 2016

Status

approved