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A302560
Partial sums of icosahedral numbers (A006564).
3
1, 13, 61, 185, 440, 896, 1638, 2766, 4395, 6655, 9691, 13663, 18746, 25130, 33020, 42636, 54213, 68001, 84265, 103285, 125356, 150788, 179906, 213050, 250575, 292851, 340263, 393211, 452110, 517390, 589496, 668888, 756041, 851445, 955605, 1069041, 1192288, 1325896
OFFSET
1,2
COMMENTS
Geometrically, the partial sums of A006564 may be interpreted as 4-dimensional icosahedral hyperpyramidal numbers.
FORMULA
a(n) = Sum_{k=1..n} A006564(k).
From Colin Barker, Aug 15 2018: (Start)
G.f.: x*(1 + 8*x + 6*x^2) / (1 - x)^5.
a(n) = n*(2 - 3*n + 10*n^2 + 15*n^3)/24.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
PROG
(PARI) Vec(x*(1 + 8*x + 6*x^2) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Aug 15 2018
(PARI) a(n) = (n*(2 - 3*n + 10*n^2 + 15*n^3)) / 24 \\ Colin Barker, Aug 15 2018
CROSSREFS
Cf. A006564.
Sequence in context: A308461 A357964 A353223 * A252970 A047673 A231800
KEYWORD
nonn,easy
AUTHOR
STATUS
approved