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 A228074 A Fibonacci-Pascal triangle read by rows: T(n,0) = Fibonacci(n), T(n,n) = n and for n > 0: T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n. 34

%I

%S 0,1,1,1,2,2,2,3,4,3,3,5,7,7,4,5,8,12,14,11,5,8,13,20,26,25,16,6,13,

%T 21,33,46,51,41,22,7,21,34,54,79,97,92,63,29,8,34,55,88,133,176,189,

%U 155,92,37,9,55,89,143,221,309,365,344,247,129,46,10,89

%N A Fibonacci-Pascal triangle read by rows: T(n,0) = Fibonacci(n), T(n,n) = n and for n > 0: T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.

%H Reinhard Zumkeller, <a href="/A228074/b228074.txt">Rows n = 0..120 of table, flattened</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%e . 0: 0

%e . 1: 1 1

%e . 2: 1 2 2

%e . 3: 2 3 4 3

%e . 4: 3 5 7 7 4

%e . 5: 5 8 12 14 11 5

%e . 6: 8 13 20 26 25 16 6

%e . 7: 13 21 33 46 51 41 22 7

%e . 8: 21 34 54 79 97 92 63 29 8

%e . 9: 34 55 88 133 176 189 155 92 37 9

%e . 10: 55 89 143 221 309 365 344 247 129 46 10

%e . 11: 89 144 232 364 530 674 709 591 376 175 56 11

%e . 12: 144 233 376 596 894 1204 1383 1300 967 551 231 67 12 .

%o a228074 n k = a228074_tabl !! n !! k

%o a228074_row n = a228074_tabl !! n

%o a228074_tabl = map fst \$ iterate

%o (\(u:_, vs) -> (vs, zipWith (+) ([u] ++ vs) (vs ++ [1]))) ([0], [1,1])

%Y Cf. A000045 (left edge), A001477 (right edge), A228078 (row sums), A027988 (maxima per row);

%Y diagonals T(*,k): A000045, A000071, A001924, A014162, A014166, A053739, A053295, A053296, A053308, A053309;

%Y diagonals T(k,*): A001477, A001245, A004006, A027927, A027928, A027929, A027930, A027931, A027932, A027933;

%Y some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A074829, A105809, A109906, A111006, A114197, A162741.

%K nonn,tabl,look

%O 0,5

%A _Reinhard Zumkeller_, Aug 15 2013

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Last modified January 18 07:38 EST 2019. Contains 319269 sequences. (Running on oeis4.)