A171451 -id:A171451 - cp's OEIS frontend

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

Paul Barry, Dec 09 2009

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

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

Cf. A130481 (first differences)

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

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.

A171450 Sequence with Hankel transform given by 2^C(n,2)*2^floor(n/3).

Original entry on oeis.org

1, 1, 2, 5, 15, 54, 231, 1133, 6082, 34397, 200063, 1180798, 7023103, 41946973, 251144922, 1505966757, 9040214223, 54314351878, 326565963479, 1964805696525, 11828911080050, 71258494789421, 429525155047263, 2590571415647886

Offset: 0

Paul Barry, Dec 09 2009

Hankel transform is A171451.

G.f.: 1/(1-x/(1-x/(1-x/(1-2x/(1-2x/(1-2x/(1-x/(1-x/(1-x/(1-2x/(1-... (continued fraction).

cp's OEIS Frontend

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

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