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A086515
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Odd positioned terms are one more than the arithmetic mean of their neighbors and the even positioned terms are one less than the arithmetic mean of their neighbors.
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2
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1, 3, 7, 9, 13, 15, 19, 21, 25, 27, 31, 33, 37, 39, 43, 45, 49, 51, 55, 57, 61, 63, 67, 69, 73, 75, 79, 81, 85, 87, 91, 93, 97, 99, 103, 105, 109, 111, 115, 117, 121, 123, 127, 129, 133, 135, 139, 141, 145, 147, 151, 153, 157, 159, 163, 165, 169, 171, 175, 177, 181, 183
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The difference of successive terms follows the pattern 2,4,2,4,2,4,2,4,2... The sequence is obtained by interleaving two arithmetic progressions with common difference 6 and the first term 1 and 3 respectively. i.e. 1,7,13,19,25,31,37,43,... 3,9,15,21,27,33,39,...
Comment from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 17 2005: This sequence can also be constructed from 3 X 3 matrices based on lucky numbers (cf. A000959). Let A=3 X 3 matrix Lucky[n+m+1], B=3 X 3 matrix Lucky[n+m+2]; M=B.A^(-1); then a(n) = unique elements of M^n*A. See Mathematica code.
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FORMULA
| a(n) + n - 2 = {a(n-1) + a(n+1)}/2.
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MATHEMATICA
| a= {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99, 105, 111, 115, 127, 129, 133, 135, 141, 151, 159, 163, 169, 171, 189, 193, 195, 201, 205, 211, 219, 223, 231, 235, 237, 241, 259, 261, 267, 273, 283, 285, 289, 297, 303, 307, 319, 321, 327, 331, 339, 349, 357, 361, 367, 385, 391, 393, 399, 409, 415, 421, 427, 429, 433, 451, 463, 475, 477, 483, 487, 489, 495, 511, 517, 519, 529, 535, 537, 541, 553, 559, 577, 579, 583, 591, 601, 613, 615 } aa = Table[a[[n + m + 1]], {n, 0, 2}, {m, 0, 2}] bb = Table[a[[n + m + 2]], {n, 0, 2}, {m, 0, 2}] M = bb.MatrixPower[aa, -1] c = Union[Flatten[Table[MatrixPower[M, n].aa, {n, 0, 200}]]] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 17 2005
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CROSSREFS
| Cf. A047241, A086515.
Sequence in context: A189561 A087550 A047241 * A132222 A111225 A032678
Adjacent sequences: A086512 A086513 A086514 * A086516 A086517 A086518
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jul 29 2003
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EXTENSIONS
| More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 10 2005
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 06 2008 at the suggestion of R. J. Mathar
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