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Triangular numbers with square pyramidal indices.
0

%I #8 Jun 17 2017 03:55:05

%S 0,1,15,105,465,1540,4186,9870,20910,40755,74305,128271,211575,335790,

%T 515620,769420,1119756,1594005,2224995,3051685,4119885,5483016,

%U 7202910,9350650,12007450,15265575,19229301,24015915,29756755,36598290

%N Triangular numbers with square pyramidal indices.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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)).

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

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

%Y Cf. A077538.

%K easy,nonn

%O 0,3

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