A076767 Triangular numbers with square pyramidal indices.

0, 1, 15, 105, 465, 1540, 4186, 9870, 20910, 40755, 74305, 128271, 211575, 335790, 515620, 769420, 1119756, 1594005, 2224995, 3051685, 4119885, 5483016, 7202910, 9350650, 12007450, 15265575, 19229301, 24015915, 29756755, 36598290

Offset

0,3

Links

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

let SP(m) be the m-th square pyramidal number m*(m+1)*(2*m+1)/6 and T(k) be the k-th Triangular number k*(k+1)/2 then a(n)=T(SP(n)).

G.f.: x*(1+8*x+21*x^2+10*x^3)/(1-x)^7. [Colin Barker, Apr 30 2012]

Example

SP(3)=14 -> a(3)=T(SP(3))=T(14)=105; SP(4)=30 -> a(4)=T(SP(4))=T(30)=465 etc

Crossrefs

Cf. A077538.

Sequence in context: A202288 A010931 A282350 * A022610 A006857 A000478

Adjacent sequences: A076764 A076765 A076766 * A076768 A076769 A076770

Keyword

easy,nonn

Author

Bruce Corrigan (scentman(AT)myfamily.com), Nov 14 2002

Status

approved