A134481 Row sums of triangle A134480.

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

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

E.g.f.: 1 + 5*exp(x)*x*(6 + 6*x + x^2)/6. - Stefano Spezia, Oct 09 2023

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 * A358632 A062158 A034133

Adjacent sequences: A134478 A134479 A134480 * A134482 A134483 A134484

Keyword

nonn,easy

Author

Gary W. Adamson, Oct 27 2007

Status

approved