A393148 - OEIS

%I #20 Mar 18 2026 23:08:27

%S 1,8,27,65,130,231,378,582,855,1210,1661,2223,2912,3745,4740,5916,

%T 7293,8892,10735,12845,15246,17963,21022,24450,28275,32526,37233,

%U 42427,48140,54405,61256,68728,76857,85680,95235,105561,116698,128687,141570,155390,170191,186018,202917,220935

%N Partial sums of truncated triangular pyramid numbers.

%C Binomial transform of [1, 7, 12, 7, 1, 0, 0, 0, ...] (with offset 0).

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (1/24)*(n-3)*(n-2)*(n^2 + 11*n - 48).

%F a(n) = Sum_{k=4..n} (k-3)*(k^2+6*k-34)/6.

%F G.f.: x^4*(1+3*x-3*x^2)/(1-x)^5.

%F E.g.f.: 3*(4 + x) - exp(x)*(12 - 9*x + 3*x^2 - x^3/2 - x^4/24). - _Stefano Spezia_, Mar 15 2026

%t a[n_]:=(1/24)*(n-3)*(n-2)*(n^2 + 11*n - 48); Array[a,44,4] (* _Stefano Spezia_, Mar 15 2026 *)

%Y Cf. A051937.

%K nonn,easy

%O 4,2

%A _Enrique Navarrete_, Mar 10 2026