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A037235 a(n) = n*(2*n^2-3*n+4)/3. 4
0, 1, 4, 13, 32, 65, 116, 189, 288, 417, 580, 781, 1024, 1313, 1652, 2045, 2496, 3009, 3588, 4237, 4960, 5761, 6644, 7613, 8672, 9825, 11076, 12429, 13888, 15457, 17140, 18941, 20864, 22913, 25092, 27405, 29856, 32449, 35188, 38077, 41120, 44321, 47684, 51213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row sums of triangle A134249. Also, binomial transform of (1, 3, 6, 4, 0, 0, 0,...). - Gary W. Adamson, Oct 15 2007

Binomial transform of a(n) starts: 0, 1, 6, 28, 112, 400, 1312, 4032, ... . - Wesley Ivan Hurt, Oct 21 2014

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.

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

FORMULA

G.f.: x*(1+3*x^2)/(1-x)^4.

a(n) = Sum_{k=0..n-1} 2*k^2+1. - Mike Warburton (mikewarb(AT)gmail.com), Sep 08 2007

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=4, a(3)=13. [Yosu Yurramendi, Sep 03 2013]

MAPLE

A037235:=n->n*(2*n^2-3*n+4)/3: seq(A037235(n), n=0..50); # Wesley Ivan Hurt, Oct 21 2014

MATHEMATICA

Table[n (2 n^2 - 3 n + 4)/3, {n, 0, 50}] (* Wesley Ivan Hurt, Oct 21 2014 *)

PROG

(PARI) A037235(n) = n*(2*n^2-3*n+4)/3 \\ Michael B. Porter, Dec 07 2009

(MAGMA) [n*(2*n^2-3*n+4)/3: n in [0..40]]; // Vincenzo Librandi, Jun 15 2011

(R)

a <- c(0, 1, 4, 13)

for(n in (length(a)+1):30) a[n] <- 4*a[n-1] -6*a[n-2] +4*a[n-3] -a[n-4]

a

[Yosu Yurramendi, Sep 03 2013]

CROSSREFS

Cf. A134249.

Sequence in context: A184632 A212747 A011936 * A051912 A060099 A208638

Adjacent sequences:  A037232 A037233 A037234 * A037236 A037237 A037238

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 17 15:28 EDT 2018. Contains 313816 sequences. (Running on oeis4.)