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A245618 Triangle {H(n,k)} similar to Pascal's with sides of 1's, but interior entries are obtained by the rule: H(n,k) = |H(n-1,k)+(-1)^m(n,k)*H(n-1,k-1)|, where m(n,k) = H(n-1,k) + H(n-1,k-1). 5
1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 4, 4, 1, 1, 1, 2, 3, 8, 3, 2, 1, 1, 1, 1, 5, 5, 1, 1, 1, 1, 2, 2, 6, 10, 6, 2, 2, 1, 1, 1, 4, 8, 16, 16, 8, 4, 1, 1, 1, 2, 3, 12, 24, 32, 24, 12, 3, 2, 1, 1, 1, 1, 9, 36, 56, 56, 36, 9, 1, 1, 1, 1, 2, 2, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Let us consider the operation <+> over integers such that k<+>m = |k+(-1)^(k+m)*m|. Then H(n,k) = H(n-1,k)<+>H(n-1,k-1).

This is an analog of the formula binomial(n,k) = binomial(n-1,k) + binomial(n-1,k-1).

LINKS

Peter J. C. Moses, First 50 rows.

EXAMPLE

Triangle begins

1

1  1

1  2  1

1  1  1  1

1  2  2  2  1

1  1  4  4  1  1

1  2  3  8  3  2  1

....................

MATHEMATICA

parityAdd[a_, b_] := Abs[a + b (-1)^(a + b)];

triangleHP[n_, 0] := 1;

triangleHP[n_, n_] := 1;

triangleHP[n_, k_] := triangleHP[n, k] = parityAdd[triangleHP[n - 1, k - 1], triangleHP[n - 1, k]];

Flatten[Table[triangleHP[n, k], {n, 0, 15}, {k, 0, n}]] (* Peter J. C. Moses, Nov 05 2014 *)

CROSSREFS

Cf. A007318, row sums in A245619, row "sums", using <+>, in A249388.

Sequence in context: A166279 A077478 A127836 * A228053 A031262 A047072

Adjacent sequences:  A245615 A245616 A245617 * A245619 A245620 A245621

KEYWORD

nonn,tabl

AUTHOR

Vladimir Shevelev, Nov 05 2014

EXTENSIONS

More terms from Peter J. C. Moses, Nov 05 2014

STATUS

approved

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Last modified October 17 01:24 EDT 2018. Contains 316275 sequences. (Running on oeis4.)