A034877 Rows of (Pascal's triangle - Losanitsch's triangle) (n >= 0, k >= 0).

1, 1, 1, 2, 2, 2, 2, 4, 4, 2, 3, 6, 10, 6, 3, 3, 9, 16, 16, 9, 3, 4, 12, 28, 32, 28, 12, 4, 4, 16, 40, 60, 60, 40, 16, 4, 5, 20, 60, 100, 126, 100, 60, 20, 5, 5, 25, 80, 160, 226, 226, 160, 80, 25, 5, 6, 30, 110, 240, 396, 452, 396, 240, 110, 30, 6, 6, 36, 140, 350, 636, 848

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• tabl
• easy

Comments

Same as A034852, but omitting the border of 0's.

Examples

			Triangle begins:
  1;
  1, 1;
  2, 2,  2;
  2, 4,  4,  2;
  3, 6, 10,  6, 3;
  3, 9, 16, 16, 9, 3;
  ...
		

References

• S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

Links

• Reinhard Zumkeller, Rows n=0..25 of triangle, flattened
• Johann Cigler, Some remarks on Rogers-Szegö polynomials and Losanitsch's triangle, arXiv:1711.03340 [math.CO], 2017.
• Johann Cigler, Some Pascal-like triangles, 2018.
• S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)
• N. J. A. Sloane, Classic Sequences
• Wikipedia, Losanitsch's triangle

Crossrefs

Cf. A007318, A034851, A034852.

Row sums are essentially A032085. Central column is A032095.

Programs

Haskell

a034877 n k = a034877_tabl !! n !! k
a034877_row n = a034877_tabl !! n
a034877_tabl = map (init . tail) $ drop 2 a034852_tabl
-- Reinhard Zumkeller, Dec 16 2013

Extensions

More terms from James Sellers, May 04 2000