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A177890 15-gonal (or pentadecagonal) pyramidal numbers:  a(n) = n*(n+1)*(13*n-10)/6. 2
0, 1, 16, 58, 140, 275, 476, 756, 1128, 1605, 2200, 2926, 3796, 4823, 6020, 7400, 8976, 10761, 12768, 15010, 17500, 20251, 23276, 26588, 30200, 34125, 38376, 42966, 47908, 53215, 58900, 64976, 71456, 78353, 85680, 93450, 101676, 110371, 119548, 129220 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also a(n) = (15-m)*A000292(n-1)+n*(n+1)*((m-2)*n-(m-5))/6 being n*(n+1)*((m-2)*n-(m-5))/6 a m-gonal pyramidal number (1<m<15). For m=6, a(n) = 9*A000292(n-1)+A002412(n).

Inverse binomial transform of this sequence: 0, 1, 14, 13, 0, 0 (0 continued).

REFERENCES

E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (thirteenth row of the table).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

G.f.: x*(1+12*x)/(1-x)^4.

a(n) = sum(i=0..n, A051867(i)).

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jul 04 2012

a(n) = sum( (n-i)*(13*i+1), i=0..n-1 ), with a(0)=0. [Bruno Berselli, Feb 10 2014]

MATHEMATICA

CoefficientList[Series[x*(1+12*x)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 04 2012 *)

PROG

(MAGMA) I:=[0, 1, 16, 58]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jul 04 2012

CROSSREFS

Cf. similar sequences listed in A237616.

Sequence in context: A235517 A253428 A005905 * A225922 A235510 A220974

Adjacent sequences:  A177887 A177888 A177889 * A177891 A177892 A177893

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Dec 14 2010

STATUS

approved

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Last modified August 18 22:05 EDT 2017. Contains 290768 sequences.