A217775 a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5).

26, 44, 68, 98, 134, 176, 224, 278, 338, 404, 476, 554, 638, 728, 824, 926, 1034, 1148, 1268, 1394, 1526, 1664, 1808, 1958, 2114, 2276, 2444, 2618, 2798, 2984, 3176, 3374, 3578, 3788, 4004, 4226, 4454, 4688, 4928, 5174, 5426, 5684, 5948, 6218, 6494, 6776, 7064

Offset: 0

Author

Jon Perry, Mar 24 2013

Keywords

• nonn
• easy

Examples

			a(1) = 1*2 + 3*4 + 5*6 = 2 + 12 + 30 = 44.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A051890 (two pairs), A217776 (4 pairs).

Programs

GAP

List([0..50], n-> (3*(2*n+5)^2 + 29)/4 ); # G. C. Greubel, Aug 27 2019

JavaScript

for (j=0;j<50;j++) {
a=j*(j+1)+(j+2)*(j+3)+(j+4)*(j+5);
document.write(a+", ");
}

Magma

[(3*(2*n+5)^2 + 29)/4: n in [0..50]]; // G. C. Greubel, Aug 27 2019

Maple

seq((3*(2*n+5)^2 + 29)/4, n=0..50); # G. C. Greubel, Aug 27 2019

Mathematica

Table[3n^2+15n+26,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1}, {26,44,68}, 50] (* Harvey P. Dale, Oct 09 2018 *)

PARI

a(n)=n*(n+1)+(n+2)*(n+3)+(n+4)*(n+5) \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(3*(2*n+5)^2 + 29)/4 for n in (0..50)] # G. C. Greubel, Aug 27 2019

Formula

G.f.: 2*(13-17*x+7*x^2)/(1-x)^3. - Bruno Berselli, Mar 29 2013

a(n) = 3*n^2 + 15*n + 26. - Bruno Berselli, Mar 29 2013

E.g.f.: (26 + 18*x + 3*x^2)*exp(x). - G. C. Greubel, Aug 27 2019

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Wesley Ivan Hurt, Jan 27 2022