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A158842 1 + n*(n+1)*(n-1)/2. 6
1, 4, 13, 31, 61, 106, 169, 253, 361, 496, 661, 859, 1093, 1366, 1681, 2041, 2449, 2908, 3421, 3991, 4621, 5314, 6073, 6901, 7801, 8776, 9829, 10963, 12181, 13486, 14881, 16369, 17953, 19636, 21421, 23311, 25309, 27418, 29641, 31981, 34441, 37024, 39733, 42571, 45541, 48646 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums of triangle A158841. Binomial transform of the sequence 1, 3, 6, 3, 0, 0, 0,...

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 1+A027480(n-1). - R. J. Mathar, Mar 28 2009

G.f.: 1-x*(-1-3*x^2+x^3) / (x-1)^4 . - R. J. Mathar, Nov 05 2011

EXAMPLE

a(4) = 31 = (1, 3, 3, 1) dot (1, 3, 6, 3) = (1 + 9 + 18 + 3). a(4) = 31 = sum of row 4 terms, triangle A158841: (13 + 9 + 6 + 3).

MAPLE

A158842 := proc(n)

1+n*(n+1)*(n-1)/2 ;

end proc:

seq(A158842(n), n=1..30) ; # R. J. Mathar, Nov 05 2011

MATHEMATICA

Table[1 + n*(n + 1)*(n - 1)/2, {n, 40}] (* and *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 13, 31}, 40] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2012 *)

PROG

(Magma) [1+ n*(n+1)*(n-1)/2: n in [1..50]]; // Vincenzo Librandi, Nov 16 2011

CROSSREFS

Cf. A158841.

Sequence in context: A335981 A191189 A106302 * A100136 A097120 A098536

Adjacent sequences: A158839 A158840 A158841 * A158843 A158844 A158845

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson & Roger L. Bagula, Mar 28 2009

STATUS

approved

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Last modified December 3 23:46 EST 2022. Contains 358544 sequences. (Running on oeis4.)