A322412 Compound tribonacci sequence with a(n) = A278041(A278040(n)), for n >= 0.

10, 34, 54, 78, 91, 115, 135, 159, 183, 203, 227, 240, 264, 284, 308, 328, 352, 365, 389, 409, 433, 457, 477, 501, 514, 538, 558, 582, 595, 619, 639, 663, 687, 707, 731, 744, 768, 788, 812, 832, 856, 869, 893, 913, 937, 961, 981, 1005, 1018, 1042, 1062, 1086, 1110, 1130, 1154, 1167, 1191, 1211, 1235

Offset: 0

Author

Wolfdieter Lang, Jan 02 2019

Keywords

• nonn
• easy

Comments

(a(n+1)) = A319971(n)-1 = A003146(A003145(n))-1, the corresponding classical compound tribonacci sequence. - Michel Dekking

The nine sequences A308199, A319967, A319968, A322410, A322409, A322411, A322413, A322412, A322414 are based on defining the tribonacci ternary word to start with index 0 (in contrast to the usual definition, in A080843 and A092782, which starts with index 1). As a result these nine sequences differ from the compound tribonacci sequences defined in A278040, A278041, and A319966-A319972. - N. J. A. Sloane, Apr 05 2019

Crossrefs

Cf. A278040, A278041, A322411.

Formula

a(n) = C(A(n)) = C(A(n) + 1) - 6 = 4*A(n) + 3*B(n) + 2*(n+3). for n >= 0, where A = A278040, B = A278039 and C = A278041. For a proof see the W. Lang link in A278040, Proposition 9, eq. (54).