A128091 Row sums of unsigned A128090.

1, 8, 45, 160, 425, 936, 1813, 3200, 5265, 8200, 12221, 17568, 24505, 33320, 44325, 57856, 74273, 93960, 117325, 144800, 176841, 213928, 256565, 305280, 360625, 423176, 493533, 572320, 660185, 757800, 865861, 985088, 1116225, 1260040, 1417325

Offset

1,2

Links

Table of n, a(n) for n=1..35.

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(n) = (n-1)*A045991(n) + n^2.

a(n) = n^2*(n^2 - 2*n + 2) = A000290(n)*A002522(n-1). - Philippe Deléham, Mar 16 2014

G.f.: x*(1 + 3*x + 15*x^2 + 5*x^3)/(1-x)^5. - Philippe Deléham, Mar 16 2014

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), a(1) = 1, a(2) = 8, a(3) = 45, a(4) = 160, a(5) = 425. - Philippe Deléham, Mar 16 2014

Example

a(4) = 160 = sum of row 4 terms of A128090: (48 + 48 + 48 + 16) = 3*A045991(4) + 4^2; where A045991 = (0, 0, 4, 18, 48, 100, ...).

Prog

(PARI) a(n)=n^2*(n^2 - 2*n + 2) \\ Charles R Greathouse IV, Oct 21 2022

Crossrefs

Cf. A000290, A002522, A128077, A128090, A045991.

Sequence in context: A210378 A247534 A100648 * A119950 A055367 A273242

Adjacent sequences: A128088 A128089 A128090 * A128092 A128093 A128094

Keyword

nonn,easy

Author

Gary W. Adamson, Feb 14 2007

Extensions

a(10)-a(35) from Philippe Deléham, Mar 16 2014

Status

approved