

A172076


a(n) = n*(n+1)*(14*n11)/6.


4



0, 1, 17, 62, 150, 295, 511, 812, 1212, 1725, 2365, 3146, 4082, 5187, 6475, 7960, 9656, 11577, 13737, 16150, 18830, 21791, 25047, 28612, 32500, 36725, 41301, 46242, 51562, 57275, 63395, 69936, 76912, 84337, 92225, 100590, 109446, 118807, 128687
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OFFSET

0,3


COMMENTS

Generated by the formula n*(n+1)*(2*d*n(2*d3))/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..n1} A001106(k) and this is the case d=7 in the identity n*(n*(d*nd+2)/2)  Sum_{k=0..n1} k*(d*kd+2)/2 = n*(n+1)*(2*d*n2*d+3)/6.
Also 16gonal (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 to sequences related to pyramidal numbers.
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+13*x)/(1x)^4.  Bruno Berselli, Dec 15 2010
a(n) = Sum_{i=0..n} A051868(i).  Bruno Berselli, Dec 15 2010
a(n) = Sum_{i=0..n1} (ni)*(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

A172076:=n>n*(n+1)*(14*n11)/6; seq(A172076(n), n=0..50); # Wesley Ivan Hurt, Feb 26 2014


MATHEMATICA

LinearRecurrence[{4, 6, 4, 1}, {0, 1, 17, 62}, 50] (* Vincenzo Librandi, Mar 01 2012 *)


PROG

(PARI) vector(40, n, n*(n1)*(14*n25)/6) \\ G. C. Greubel, Aug 30 2019
(Magma) [n*(n+1)*(14*n11)/6: n in [0..40]] // G. C. Greubel, Aug 30 2019
(Sage) [n*(n+1)*(14*n11)/6 for n in (0..40)] # G. C. Greubel, Aug 30 2019
(GAP) List([0..40], n> n*(n+1)*(14*n11)/6); # G. C. Greubel, Aug 30 2019


CROSSREFS

Cf. similar sequences listed in A237616.
Sequence in context: A226026 A195025 A010005 * A063522 A244973 A145850
Adjacent sequences: A172073 A172074 A172075 * A172077 A172078 A172079


KEYWORD

nonn,easy


AUTHOR

Vincenzo Librandi, Jan 25 2010


STATUS

approved



