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A125127
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Array L(k,n) read by antidiagonals: k-step Lucas numbers.
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3
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1, 1, 1, 1, 3, 1, 1, 3, 7, 1, 1, 3, 7, 11, 1, 1, 3, 7, 11, 18, 1, 1, 3, 7, 15, 21, 29, 1, 1, 3, 7, 15, 39, 47, 1, 1, 3, 7, 15, 31, 51, 71, 76, 1, 1, 3, 7, 15, 31, 57, 99, 131, 123, 1, 1, 3, 7, 15, 31, 63, 113, 191, 241, 199
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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LINKS
| Eric Weisstein's World of Mathematics, Lucas n-Step Number
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FORMULA
| L(k,n) = L(k,n-1) + L(k,n-2) + ... + L(k,n-k); L(k,1) = 1 and for n<=0, L(k,n) = 0.
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EXAMPLE
| Table begins:
1.|.1..1..1...1...1...1....1....1....1....1.
2.|.1..3..7..11..18..29...47...76..123..199.
3.|.1..3..7..11..21..39...71..131..241..443.
4.|.1..3..7..15..26..51...99..191..367..708.
5.|.1..3..7..15..31..57..113..223..439..863.
6.|.1..3..7..15..31..63..120..239..475..943.
7.|.1..3..7..15..31..63..127..247..493..983.
8.|.1..3..7..15..31..63..127..255..502.1003.
9.|.1..3..7..15..31..63..127..255..511.1013.
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CROSSREFS
| n-step Lucas number analogue of A092921 Array F(k, n) read by antidiagonals: k-generalized Fibonacci numbers (and see related A048887, A048888). L(1, n) = "1-step Lucas numbers" = A000012. L(2, n) = 2-step Lucas numbers = A000204. L(3, n) = 3-step Lucas numbers = A001644. L(4, n) = 4-step Lucas numbers = A001648 Tetranacci numbers A073817 without the leading term 4. L(5, n) = 5-step Lucas numbers = A074048 Pentanacci numbers with initial conditions a(0)=5, a(1)=1, a(2)=3, a(3)=7, a(4)=15. L(6, n) = 6-step Lucas numbers = A074584 Esanacci ("6-anacci") numbers. L(7, n) = 7-step Lucas numbers = A104621 Heptanacci-Lucas numbers. L(8, n) = 8-step Lucas numbers = A105754. L(9, n) = 9-step Lucas numbers = A105755. See A000295, A125129 for comments on partial sums of diagonals.
Cf. A000012, A000032, A000204, A001644, A001648, A048887, A048888, A074048, A074584, A092921, A104621, A105754, A105755, A125129.
Sequence in context: A114588 A121745 A089312 * A058735 A107294 A161788
Adjacent sequences: A125124 A125125 A125126 * A125128 A125129 A125130
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 21 2006
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