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

1,2

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A271771 A270990 A272558 * A263318 A011845 A099450

Adjacent sequences: A081489 A081490 A081491 * A081493 A081494 A081495

Keyword

nonn,easy

Author

Amarnath Murthy, Mar 25 2003

Extensions

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

Formula corrected by Colin Barker, Jul 28 2012

Status

approved