OFFSET
1,2
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Wikipedia, Pyramidal number
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = (n*(4+3*n-n^2))/6.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: x*(1 - 2*x) / (x-1)^4.
EXAMPLE
G.f. = x + 2*x^2 + 2*x^3 - 5*x^5 - 14*x^6 - 28*x^7 - 48*x^8 - 75*x^9 + ...
MATHEMATICA
Table[(n*(4+3*n-n^2))/6, {n, 1, 60}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 2, 2, 0}, 60] (* G. C. Greubel, Aug 03 2018 *)
PROG
(PARI) ppg(r, n) = (3*n^2+n^3*(r-2)-n*(r-5))/6
vector(100, n, ppg(1, n))
(Magma) [(n*(4+3*n-n^2))/6: n in [1..60]]; // G. C. Greubel, Aug 03 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Colin Barker, Feb 07 2015
STATUS
approved