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A101102 Fifth partial sums of cubes (A000578). 15
1, 13, 82, 354, 1200, 3432, 8646, 19734, 41613, 82225, 153868, 274924, 472056, 782952, 1259700, 1972884, 3016497, 4513773, 6624046, 9550750, 13550680, 18944640, 26129610, 35592570, 47926125, 63846081, 84211128, 110044792, 142559824, 183185200, 233595912 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

FORMULA

a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(10 + 3*n*(n+5))/20160.

This sequence could be obtained from the general formula a(n) = n*(n+1)*(n+2)*(n+3)*...*(n+k)*(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=5. - Alexander R. Povolotsky, May 17 2008

G.f.: x*(x^2+4*x+1) / (1-x)^9. - Colin Barker, Apr 23 2015

MATHEMATICA

Table[binomial[n+5, 6]*(3*n^2+15*n+10)/28, {n, 1, 30}] (* G. C. Greubel, Dec 01 2018 *)

PROG

(PARI) a(n)=sum(t=1, n, sum(s=1, t, sum(l=1, s, sum(j=1, l, sum(m=1, j, sum(i=m*(m+1)/2-m+1, m*(m+1)/2, (2*i-1))))))) \\ Alexander R. Povolotsky, May 17 2008

(PARI) Vec(-x*(x^2+4*x+1)/(x-1)^9 + O(x^100)) \\ Colin Barker, Apr 23 2015

(PARI) a(n) = binomial(n+5, 6)*(3*n^2+15*n+10)/28 \\ Charles R Greathouse IV, Apr 23 2015

(MAGMA) [Binomial(n+5, 6)*(3*n^2+15*n+10)/28: n in [1..30]]; // G. C. Greubel, Dec 01 2018

(Sage) [binomial(n+5, 6)*(3*n^2+15*n+10)/28 for n in  (1..30)] # G. C. Greubel, Dec 01 2018

CROSSREFS

Cf. A000537, A024166, A101094. Partial sums of A101097.

Sequence in context: A241696 A052255 A082203 * A213572 A142085 A163688

Adjacent sequences:  A101099 A101100 A101101 * A101103 A101104 A101105

KEYWORD

easy,nonn

AUTHOR

Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

EXTENSIONS

Edited by Ralf Stephan, Dec 16 2004

STATUS

approved

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Last modified October 14 06:55 EDT 2019. Contains 327995 sequences. (Running on oeis4.)