|
| |
|
|
A264854
|
|
a(n) = n*(n + 1)*(11*n^2 + 11*n - 10)/24.
|
|
3
|
|
|
|
0, 1, 14, 61, 175, 400, 791, 1414, 2346, 3675, 5500, 7931, 11089, 15106, 20125, 26300, 33796, 42789, 53466, 66025, 80675, 97636, 117139, 139426, 164750, 193375, 225576, 261639, 301861, 346550, 396025, 450616, 510664, 576521, 648550, 727125, 812631, 905464, 1006031
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Partial sums of centered 11-gonal (or hendecagonal) pyramidal numbers.
|
|
|
LINKS
|
Table of n, a(n) for n=0..38.
OEIS Wiki, Figurate numbers
Eric Weisstein's World of Mathematics, Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
|
|
|
FORMULA
|
G.f.: x*(1 + 9*x + x^2)/(1 - x)^5.
a(n) = Sum_{k = 0..n} A004467(k).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Vincenzo Librandi, Nov 27 2015
|
|
|
MATHEMATICA
|
Table[n (n + 1) (11 n^2 + 11 n - 10)/24, {n, 0, 50}]
|
|
|
PROG
|
(Magma) [n*(n+1)*(11*n^2+11*n-10)/24: n in [0..50]]; // Vincenzo Librandi, Nov 27 2015
(PARI) a(n)=n*(n+1)*(11*n^2+11*n-10)/24 \\ Charles R Greathouse IV, Jul 26 2016
|
|
|
CROSSREFS
|
Cf. A004467.
Cf. similar sequences provided by the partial sums of centered k-gonal pyramidal numbers: A006522 (k=1), A006007 (k=2), A002817 (k=3), A006325 (k=4), A006322 (k=5), A000537 (k=6), A006323 (k=7), A006324 (k=8), A236770 (k=9), A264853 (k=10), this sequence (k=11), A062392 (k=12), A264888 (k=13).
Sequence in context: A051799 A164540 A140184 * A189948 A252255 A025415
Adjacent sequences: A264851 A264852 A264853 * A264855 A264856 A264857
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
Ilya Gutkovskiy, Nov 26 2015
|
|
|
STATUS
|
approved
|
| |
|
|
