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A134481 Row sums of triangle A134480. 3
1, 5, 20, 50, 100, 175, 280, 420, 600, 825, 1100, 1430, 1820, 2275, 2800, 3400, 4080, 4845, 5700, 6650, 7700, 8855, 10120, 11500, 13000, 14625, 16380, 18270, 20300, 22475, 24800, 27280, 29920, 32725, 35700, 38850, 42180, 45695 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of [1, 4, 11, 4, 1, -1, 1, -1, 1, -1,...]. Also, 1 followed by 5 * A000292, the tetrahedral numbers; i.e. 1, then 5 * (1, 4, 10, 25, 35,...).

If Y is a 5-subset of an n-set X then, for n>=8, a(n-7) is the number of 4-subsets of X having exactly one element in common with Y. - Milan Janjic, Dec 28 2007

LINKS

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

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

FORMULA

a(n) = 5*binomial(n+2,3) for n>0. - Milan Janjic, Dec 28 2007

G.f. 1 + 5*x / (1-x)^4.- R. J. Mathar, Apr 04 2012

a(n) = sum( i=0..n, (n+i)*(1+i) ) for n>0. [Bruno Berselli, Dec 16 2013]

EXAMPLE

a(2) = 20 = sum of row 3 terms of triangle A134480: (9 + 7 + 4).

a(3) = 50 = (1, 3, 3, 1) dot (1, 4, 11, 4) = (1 + 12 + 33 + 4).

a(2) = 20 = 2*1 + 3*2 + 4*3; a(5) = 5*1 + 6*2 + 7*3 + 8*4 + 9*5 + 10*6. [Bruno Berselli, Dec 16 2013]

MATHEMATICA

CoefficientList[Series[1+5x/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2012 *)

PROG

(MAGMA) I:=[1, 5, 20, 50, 100]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 29 2012

CROSSREFS

Cf. A134480, A000292.

Sequence in context: A147488 A297569 A190094 * A062158 A034133 A006504

Adjacent sequences:  A134478 A134479 A134480 * A134482 A134483 A134484

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Oct 27 2007

STATUS

approved

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Last modified October 19 15:34 EDT 2021. Contains 348091 sequences. (Running on oeis4.)