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A158842
a(n) = 1 + n*(n+1)*(n-1)/2.
8
1, 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
OFFSET
0,3
COMMENTS
Binomial transform of the sequence 1, 0, 3, 3, 0, 0, 0, ... .
FORMULA
a(n) = 1+A027480(n-1) for 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
E.g.f.: exp(x)*(1 + x^3/2 + 3*x^2/2). - Nikolaos Pantelidis, Feb 13 2023
EXAMPLE
a(4) = 31 = sum of row 4 terms of triangle A158841: (13 + 9 + 6 + 3).
MAPLE
A158842 := proc(n)
1+n*(n+1)*(n-1)/2 ;
end proc:
seq(A158842(n), n=0..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
Row sums of A158841.
Sequence in context: A335981 A191189 A106302 * A100136 A097120 A098536
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0)=1 prepended by Andrew Howroyd, Feb 14 2023
STATUS
approved