cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A322409 Compound tribonacci sequence with a(n) = A278040(A278040(n)), for n >= 0.

Original entry on oeis.org

5, 18, 29, 42, 49, 62, 73, 86, 99, 110, 123, 130, 143, 154, 167, 178, 191, 198, 211, 222, 235, 248, 259, 272, 279, 292, 303, 316, 323, 336, 347, 360, 373, 384, 397, 404, 417, 428, 441, 452, 465, 472, 485, 496, 509, 522, 533, 546, 553, 566, 577, 590, 603, 614, 627, 634, 647, 658, 671, 682, 695
Offset: 0

Views

Author

Wolfdieter Lang, Jan 02 2019

Keywords

Comments

(a(n+1)) = A319968(n)-1 = A003145(A003145(n))-1, the corresponding classical compound tribonacci sequence. - Michel Dekking, Apr 04 2019
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. A278039, A278040, A322408.
Cf. A003144, A003145, A003146.

Formula

a(n) = A(A(n)) = A(A(n) + 1) - 3 = 2*(A(n) + B(n)) + n + 3, for n >= 0, where A = A278040 and B = A278039. For a proof see the W. Lang link in A278040, Proposition 9, eq. (48).

A172515 First differences of A172513.

Original entry on oeis.org

3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3
Offset: 1

Views

Author

Stephen Crowley, Feb 05 2010

Keywords

Comments

This sequence appears to have only '3's and '4's. Indices of '4's seem to be given by A322408, but this is true only for n < 95: then the next term in A322408 is 95, but only a(96) = 4. - M. F. Hasler, Apr 19 2019

Crossrefs

Cf. A172513, A167389.

Programs

Extensions

Keyword "hard" removed by M. F. Hasler, Apr 11 2019

A321333 Compound sequence with a(n) = A319198(A278040(n)), for n >= 0.

Original entry on oeis.org

1, 4, 5, 8, 9, 12, 13, 16, 19, 20, 23, 24, 27, 28, 31, 32, 35, 36, 39, 40, 43, 46, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 69, 70, 73, 74, 77, 78, 81, 82, 85, 86, 89, 90, 93, 96, 97, 100, 101, 104, 105, 108, 111, 112, 115, 116, 119, 120, 123, 124, 127
Offset: 0

Views

Author

Wolfdieter Lang, Dec 27 2018

Keywords

Comments

Old name was: Compound tribonacci sequence a(n) = A319198(A278040(n)), for n >= 0.
a(n) gives the sum of the entries of the tribonacci word sequence t = A080843 not exceeding t(A(n)), with A(n) = A278040(n).

Examples

			n = 4, A(4) = 14, t = {0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, ...}, which sums to  9  = a(4) = 2*(14 - 7) - 5, because B(4) = 7.

Crossrefs

Cf. A080843, A278040, A278039, A319198, A322407, A322408.

Formula

a(n) = z(A(n)) = Sum_{j=0..A(n)} t(j), n >= 0, with z = A319198, A = A278040 and t = A080843.
a(n) = 2*(A(n) - B(n)) - (n + 1), where B(n) = A278039(n). For a proof see the W. Lang link in A080843, Proposition 8, eq. (45).
a(n)= 1 + Sum_{k=1..n-1} d(k), where d is the tribonacci sequence on the alphabet {3,1,1}. - Michel Dekking, Oct 08 2019

Extensions

Name changed by Michel Dekking, Oct 08 2019

A322407 Compound sequence a(n) = A319198(A278039(n)), for n >= 0.

Original entry on oeis.org

0, 1, 3, 4, 4, 5, 7, 8, 9, 11, 12, 12, 13, 15, 16, 18, 19, 19, 20, 22, 23, 24, 26, 27, 27, 28, 30, 31, 31, 32, 34, 35, 36, 38, 39, 39, 40, 42, 43, 45, 46, 46, 47, 49, 50, 51, 53, 54, 54, 55, 57, 58, 59, 61, 62, 62, 63, 65, 66, 68, 69
Offset: 0

Views

Author

Wolfdieter Lang, Jan 02 2019

Keywords

Comments

Old name was: Compound tribonacci sequence a(n) = A319198(A278039(n)), for n >= 0.
a(n) gives the sum of the entries of the tribonacci word sequence t = A080843 not exceeding t(B(n)), with B(n) = A278039(n).

Examples

			n = 3: B(3) = 6, t = {0, 1, 0, 2, 0, 1, 0, ...} which sums to 4 = a(3) = -12 + 3*6 - 2, because A(3) = 12.

Crossrefs

Cf. A080843, A278040, A278039, A319198, A321333, A322408.

Formula

a(n) = z(B(n)) = Sum_{j=0..B(n)} t(j), n >= 0, with z = A319198, B = A278039 and t = A080843.
a(n) = -A(n) + 3*B(n) - (n - 1), where A(n) = A278040(n). For a proof see the W. Lang link in A080843, Proposition 8, eq. (46).
a(n) = Sum_{k=1..n-1} d(k), where d is the tribonacci sequence on the alphabet {1,2,0}. - Michel Dekking, Oct 08 2019

Extensions

Name changed by Michel Dekking, Oct 07 2019
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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