OFFSET
1,2
COMMENTS
Sums of hexagonal numbers (A000384) in successive groups of length 1,2,3,etc, so 1, 6+15, 28+45+66, 91+120+153+190, etc.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Stefano Spezia, May 12 2024: (Start)
G.f.: x*(1 + 15*x + 28*x^2 + 15*x^3 + x^4)/(1 - x)^6.
E.g.f.: exp(x)*x*(6 + 57*x + 79*x^2 + 30*x^3 + 3*x^4)/6. (End)
EXAMPLE
The hexagonal numbers and their groups summed begin
1, 6, 15, 28, 45, 66, 91, 120, 153, 190
\/ \---/ \--------/ \---------------/
1, 21, 139, 554
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Kelvin Voskuijl, May 12 2024
STATUS
approved