A171452 a(n) = C(n,2) + floor(n/3).

0, 0, 1, 4, 7, 11, 17, 23, 30, 39, 48, 58, 70, 82, 95, 110, 125, 141, 159, 177, 196, 217, 238, 260, 284, 308, 333, 360, 387, 415, 445, 475, 506, 539, 572, 606, 642, 678, 715, 754, 793, 833, 875, 917, 960, 1005, 1050, 1096, 1144, 1192, 1241, 1292, 1343, 1395

Offset: 0

Author

Paul Barry, Dec 09 2009

Keywords

• easy
• nonn

Comments

Exponents in Hankel transform A171451.

For n>=2 a(n) is the smallest addend in the sums of n terms where all the natural numbers are used once 1+2=3, 4+5+6=15, 7+8+9+10=34, 11+12+13+14+16=66, 17+18+19+20+21+22=117 23+24+25+26+27+28+29=182, 30+31+32+33+35+36+37+38=272. - Anton Zakharov, Aug 28 2016

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Crossrefs

Cf. A130481 (first differences)

Programs

PARI

a(n)=n*(3*n-1)\6 \\ Charles R Greathouse IV, Aug 28 2016

Formula

G.f.: (1+2x)/((1-x)^3*(1+x+x^2));

a(n) = (3n^2-n-2)/6 + sqrt(3)*cos(2*Pi*n/3+Pi/6)/9 + sin(2*Pi*n/3+Pi/6)/3.