OFFSET
0,3
COMMENTS
Generated by the formula n*(n+1)*(2*d*n-(2*d-3))/6 for d=7.
From Bruno Berselli, Dec 14 2010: (Start)
In fact, the sequence is related to A001106 by a(n) = n*A001106(n) - Sum_{k=0..n-1} A001106(k) and this is the case d=7 in the identity n*(n*(d*n-d+2)/2) - Sum_{k=0..n-1} k*(d*k-d+2)/2 = n*(n+1)*(2*d*n-2*d+3)/6.
Also 16-gonal (or hexadecagonal) pyramidal numbers.
Inverse binomial transform of this sequence: 0, 1, 15, 14, 0, 0 (0 continued). (End)
REFERENCES
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93. [From Bruno Berselli, Feb 13 2014]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
B. Berselli, A description of the recursive method in Comments lines: website Matem@ticamente (in Italian), 2008.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: x*(1+13*x)/(1-x)^4. - Bruno Berselli, Dec 15 2010
a(n) = Sum_{i=0..n} A051868(i). - Bruno Berselli, Dec 15 2010
a(n) = Sum_{i=0..n-1} (n-i)*(14*i+1), with a(0)=0. - Bruno Berselli, Feb 10 2014
E.g.f.: x*(6 + 45*x + 14*x^2)*exp(x)/6. - G. C. Greubel, Aug 30 2019
MAPLE
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 17, 62}, 50] (* Vincenzo Librandi, Mar 01 2012 *)
PROG
(PARI) vector(40, n, n*(n-1)*(14*n-25)/6) \\ G. C. Greubel, Aug 30 2019
(Magma) [n*(n+1)*(14*n-11)/6: n in [0..40]] // G. C. Greubel, Aug 30 2019
(Sage) [n*(n+1)*(14*n-11)/6 for n in (0..40)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..40], n-> n*(n+1)*(14*n-11)/6); # G. C. Greubel, Aug 30 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 25 2010
STATUS
approved