A147874 a(n) = (5*n-7)*(n-1).

0, 3, 16, 39, 72, 115, 168, 231, 304, 387, 480, 583, 696, 819, 952, 1095, 1248, 1411, 1584, 1767, 1960, 2163, 2376, 2599, 2832, 3075, 3328, 3591, 3864, 4147, 4440, 4743, 5056, 5379, 5712, 6055, 6408, 6771, 7144, 7527, 7920, 8323, 8736, 9159, 9592, 10035

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Nov 16 2008

Keywords

• nonn
• easy

Comments

Zero followed by partial sums of A017305.

Appears to be related to various other sequences: a(n) = A036666(2*n-2) for n>1; a(n) = A115006(2*n-3) for n>1; a(n) = A118015(5*n-6) for n>1; a(n) = A008738(5*n-7) for n>1.

Even dodecagonal numbers divided by 4. - Omar E. Pol, Aug 19 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..2000
• Leo Tavares, Illustration: Triangular Badges
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A017305 (10n+3), A036666, A115006, A118015 (floor(n^2/5)), A008738 (floor((n^2+1)/5)), A294830.

Cf. A051624, A193872. - Omar E. Pol, Aug 19 2011

Cf. A014105, A002378.

Programs

GAP

List([1..50], n-> (5*n-7)*(n-1)); # G. C. Greubel, Jul 30 2019

Magma

[ 0 ] cat [ &+[ 10*k+3: k in [0..n-1] ]: n in [1..50] ]; // Klaus Brockhaus, Nov 17 2008

Magma

[ 5*n^2-2*n: n in [0..50] ];

Mathematica

s=0;lst={s};Do[s+=n++ +3;AppendTo[lst,s],{n,0,6!,10}];lst
Table[5n^2-12n+7,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{0,3,16},50] (* or *) PolygonalNumber[12,Range[0,100,2]]/4 (* Harvey P. Dale, Aug 08 2021 *)

PARI

{m=50; a=7; for(n=0, m, print1(a=a+10*(n-1)+3, ","))} \\ Klaus Brockhaus, Nov 17 2008

Sage

[(5*n-7)*(n-1) for n in (1..50)] # G. C. Greubel, Jul 30 2019

Formula

a(n) = Sum_{k=0..n-2} 10*k+3 = Sum_{k=0..n-2} A017305(k).

G.f.: x*(3 + 7*x)/(1-x)^3.

a(n) = 10*(n-2) + 3 + a(n-1).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = A193872(n-1)/4. - Omar E. Pol, Aug 19 2011

a(n+1) = A131242(10n+2). - Philippe Deléham, Mar 27 2013

E.g.f.: -7 + (7 - 7*x + 5*x^2)*exp(x). - G. C. Greubel, Jul 30 2019

Sum_{n>=2} 1/a(n) = A294830. - Amiram Eldar, Nov 15 2020

a(n) = A014105(n-1) + 3*A002378(n-2). - Leo Tavares, Mar 31 2025

Extensions

Edited by R. J. Mathar and Klaus Brockhaus, Nov 17 2008, Nov 20 2008