|
| |
|
|
A289721
|
|
Let a(0)=1. Then a(n) = sums of consecutive strings of positive integers of length 3*n, starting with the integer 2.
|
|
1
|
|
|
|
1, 9, 45, 135, 306, 585, 999, 1575, 2340, 3321, 4545, 6039, 7830, 9945, 12411, 15255, 18504, 22185, 26325, 30951, 36090, 41769, 48015, 54855, 62316, 70425, 79209, 88695, 98910, 109881, 121635, 134199, 147600, 161865, 177021, 193095, 210114, 228105, 247095, 267111, 288180
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
G.f.: (1 + 5*x + 15*x^2 + 5*x^3 + x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 4.
(End)
|
|
|
EXAMPLE
|
1, 2 + 3 + 4, 5 + 6 + 7 + 8 + 9 + 10, ...
|
|
|
MATHEMATICA
|
CoefficientList[Series[(1 + 5 x + 15 x^2 + 5 x^3 + x^4)/(1 - x)^4, {x, 0, 40}], x] (* Michael De Vlieger, Aug 15 2017 *)
|
|
|
PROG
|
(PARI) Vec((1 + 5*x + 15*x^2 + 5*x^3 + x^4) / (1 - x)^4 + O(x^100)) \\ Colin Barker, Aug 14 2017
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
