A317790 a(n) = 2*a(n-1) - a(n-2) + a(n-4) - 2*(n-5) + a(n-6) for n>5, a(0)=a(1)=1, a(2)=a(3)=7, a(4)=13, a(5)=19.

1, 1, 7, 7, 13, 19, 31, 37, 49, 61, 79, 91, 109, 127, 151, 169, 193, 217, 247, 271, 301, 331, 367, 397, 433, 469, 511, 547, 589, 631, 679, 721, 769, 817, 871, 919, 973, 1027, 1087, 1141, 1201, 1261, 1327, 1387, 1453, 1519, 1591, 1657, 1729, 1801, 1879, 1951

Offset

0,3

Comments

a(n) is b(2*n) in A215175.

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).

Formula

G.f.: (1 - x + 6*x^2 - 6*x^3 + 5*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)). - Colin Barker, Aug 07 2018

a(n+1) = a(n) + 6*A059169(n+1).

a(2*k+1) = A003215(k).

From Bruno Berselli, Jul 08 2018: (Start)

a(2*k) = A016921(A000982(k)). More generally:

a(n) = (6*n^2 + 3*(3 - 2*(-1)^(n/2))*(1 + (-1)^n) + 2)/8. (End)

Mathematica

CoefficientList[Series[(1 - x + 6 x^2 - 6 x^3 + 5 x^4 + x^5)/((1 - x)^3*(1 + x) (1 + x^2)), {x, 0, 51}], x] (* Michael De Vlieger, Aug 07 2018 *)
Table[(6 n^2 + 3 (3 - 2 (-1)^(n/2)) (1 + (-1)^n) + 2)/8, {n, 0, 60}] (* Bruno Berselli, Aug 08 2018 *)

Prog

(PARI) Vec((1 - x + 6*x^2 - 6*x^3 + 5*x^4 + x^5) / ((1 - x)^3*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Aug 07 2018

Crossrefs

Cf. A003215, A059169, A131729 (reverse order), A215175.

Cf. A000982, A016921.

Sequence in context: A072821 A038589 A332304 * A109539 A109541 A173314

Adjacent sequences: A317787 A317788 A317789 * A317791 A317792 A317793

Keyword

nonn,easy

Author

Paul Curtz, Aug 07 2018

Extensions

Incorrect term 837 replaced with 817 by Colin Barker, Aug 07 2018

More terms from Colin Barker, Aug 07 2018

Status

approved