A329757 Doubly octagonal pyramidal numbers.

0, 1, 765, 27435, 345415, 2469420, 12352956, 48294610, 157609530, 447989355, 1141711615, 2663460261, 5775482505, 11777133550, 22789550070, 42150245460, 74946834916, 128723876325, 214401953745, 347453633935, 549386792955, 849592039296, 1287617552320, 1915941609990, 2803320397950, 4038796372975

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Index to sequences related to pyramidal numbers

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

G.f.: x*(1 + 755*x + 19830*x^2 + 105370*x^3 + 158255*x^4 + 70629*x^5 + 7930*x^6 + 110*x^7)/(1 - x)^10.

a(n) = A002414(A002414(n)).

a(n) = Sum_{k=0..A002414(n)} A000567(k).

a(n) = n *(2*n-1) *(n+1) *(2*n^3+n^2-n+2) *(2*n^3+n^2-n-1) /8 . - R. J. Mathar, Nov 28 2019

Mathematica

A002414[n_] := n (n + 1) (2 n - 1)/2; a[n_] := A002414[A002414[n]]; Table[a[n], {n, 0, 25}]
Table[Sum[k (3 k - 2), {k, 0, n (n + 1) (2 n - 1)/2}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[x (1 + 755 x + 19830 x^2 + 105370 x^3 + 158255 x^4 + 70629 x^5 + 7930 x^6 + 110 x^7)/(1 - x)^10, {x, 0, nmax}], x]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 765, 27435, 345415, 2469420, 12352956, 48294610, 157609530, 447989355}, 26]

Crossrefs

Cf. A000567, A002414, A140236, A264892, A329753, A329754, A329755, A329756.

Sequence in context: A158126 A124413 A319741 * A127206 A343704 A343705

Adjacent sequences: A329754 A329755 A329756 * A329758 A329759 A329760

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Nov 20 2019

Status

approved