A081492 Sum of terms in n-th row of A081491.

1, 5, 18, 54, 135, 291, 560, 988, 1629, 2545, 3806, 5490, 7683, 10479, 13980, 18296, 23545, 29853, 37354, 46190, 56511, 68475, 82248, 98004, 115925, 136201, 159030, 184618, 213179, 244935, 280116, 318960, 361713, 408629, 459970, 516006, 577015

Offset: 1

Author

Amarnath Murthy, Mar 25 2003

Keywords

• nonn
• easy

Comments

For odd n a(n) is a multiple of n and a(n)/n is the middle term of the corresponding row.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A002522, A005408, A081489, A081490, A081491.

Programs

GAP

List([1..40], n-> n*(2*(n-1)^3+7*n-1)/6); # G. C. Greubel, Aug 13 2019

Magma

[n*(2*(n-1)^3+7*n-1)/6: n in [1..40]]; // G. C. Greubel, Aug 13 2019

Maple

seq(n*(2*(n-1)^3+7*n-1)/6, n=1..40); # G. C. Greubel, Aug 13 2019

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{1,5,18,54,135},40] (* Harvey P. Dale, Jul 01 2018 *)

PARI

vector(40, n, n*(2*(n-1)^3+7*n-1)/6) \\ G. C. Greubel, Aug 13 2019

Sage

[n*(2*(n-1)^3+7*n-1)/6 for n in (1..40)] # G. C. Greubel, Aug 13 2019

Formula

a(n) = n*(2*n^3 - 6*n^2 + 13*n - 3)/6.

G.f.: x*(1+x)*(1-x+4*x^2)/(1-x)^5. - Colin Barker, Jul 28 2012

E.g.f.: x*(6 +9*x +6*x^2 +2*x^3)/6. - G. C. Greubel, Aug 13 2019

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003.

Formula corrected by Colin Barker, Jul 28 2012