A256857 a(n) = n*(n^2 + 3*n - 2)/2.

0, 1, 8, 24, 52, 95, 156, 238, 344, 477, 640, 836, 1068, 1339, 1652, 2010, 2416, 2873, 3384, 3952, 4580, 5271, 6028, 6854, 7752, 8725, 9776, 10908, 12124, 13427, 14820, 16306, 17888, 19569, 21352, 23240, 25236, 27343, 29564, 31902, 34360, 36941, 39648, 42484, 45452, 48555

Offset: 0

Author

Luciano Ancora, Apr 11 2015

Keywords

• nonn
• easy

Comments

The sequence is the 5th upper diagonal of the array in A139600.

Links

• Eric Weisstein's World of Mathematics, Polygonal Number
• Index to sequences related to polygonal numbers
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A057145, A139600.

Programs

Magma

[n*(n^2+3*n-2)/2: n in [0..50]]; // Vincenzo Librandi, Apr 14 2015

Mathematica

Table[n (n^2 + 3 n - 2)/2, {n, 0, 40}]

PARI

vector(50, n, n--; n*(n^2+3*n-2)/2) \\ Bruno Berselli, Apr 15 2015

Formula

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

a(n) = A057145(n+6,n). - R. J. Mathar, Jul 28 2016

a(n) = Sum_{i=1..n} (n-i-1) mod (n+1). - Wesley Ivan Hurt, Sep 15 2017

E.g.f.: exp(x)*x*(2 + 6*x + x^2)/2. - Stefano Spezia, Jan 20 2024

Extensions

a(41)-a(45) from Stefano Spezia, Jan 20 2024