This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 16 11:32 EST 2019. Contains 319188 sequences. (Running on oeis4.)