A255261 -id:A255261 - cp's OEIS frontend

A100963 a(1)=1. a(n) = a(n-1) + sum of the triangular numbers which are among the first (n-1) terms of the sequence.

1, 2, 3, 7, 11, 15, 34, 53, 72, 91, 201, 311, 421, 531, 641, 751, 861, 1832, 2803, 3774, 4745, 5716, 6687, 7658, 8629, 9600, 10571, 11542, 12513, 13484, 14455, 15426, 16397, 17368, 18339, 19310, 20281, 21252, 22223, 23194, 24165, 25136, 26107, 27078, 28049

Offset: 1

Leroy Quet, Jun 07 2007

nonn

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A129895.

Cf. A101135, A255260, A255261.

Nest[Append[#, Last@ # + Total@ Select[#, IntegerQ@ First@ Values@ Last@ Solve[x (x + 1)/2 == #, x] &]] &, {1}, 44] (* Michael De Vlieger, Sep 24 2017 *)

vector(100, n, if(n==1, a_n_1=sum_=1, a_n_1+=sum_; if(ispolygonal(a_n_1, 3), sum_+=a_n_1)); a_n_1) \\ Colin Barker, Feb 19 2015

More terms from Robert Gerbicz, Jun 10 2007

A255260 a(n) = a(n-1) + sum of the pentagonal numbers which are among the first (n-1) terms of the sequence, with a(1)=1.

Original entry on oeis.org

1, 2, 3, 4, 5, 11, 17, 23, 29, 35, 76, 117, 275, 433, 591, 749, 907, 1065, 1223, 1381, 1539, 1697, 1855, 2013, 2171, 2329, 2487, 2645, 2803, 2961, 3119, 3277, 3435, 3593, 3751, 3909, 4067, 4225, 4383, 4541, 4699, 4857, 5015, 5173, 5331, 5489, 5647, 5805

Offset: 1

Colin Barker, Feb 19 2015

nonn

			a(7) = 17 because a(6) = 11, pentagonal numbers already in the sequence are 1 and 5, and 11+1+5 = 17.

Colin Barker, Table of n, a(n) for n = 1..1000

Cf. A100963, A101135, A255261.

vector(100, n, if(n==1, a_n_1=sum_=1, a_n_1+=sum_; if(ispolygonal(a_n_1, 5), sum_+=a_n_1)); a_n_1)

cp's OEIS Frontend

A100963 a(1)=1. a(n) = a(n-1) + sum of the triangular numbers which are among the first (n-1) terms of the sequence.

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