1,2

Also variance of (i.e. expectation of the square of) area under a random walk with 2n steps whose first return to the origin is at point 2n. - Henry Bottomley (se16(AT)btinternet.com), Apr 11 2002

Also number of numbers to be checked for primality in the n X n generalization of the Gordon Lee puzzle (see A109943). - Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 09 2005

n^2 + 4*(n+1)*Sum {(n-j-1); j=0..n-1} + 8*Sum {(n-k-j-1); j=0..n-2, k=1..n-1-j}.

a(n) =n(2n-1)(5n-2)/3 - Henry Bottomley (se16(AT)btinternet.com), Apr 11 2002

For n=2, from the array

ab

cd

we get 16 words: a,b,c,d,ab,ba,cd,dc,ac,ca,bd,db,ad,da,cb,bc.

For n=3, from abc/def/ghi we get 9 of length 1, 40 of length 2, 16 of length 3, a total of 65.

Gordon Lee puzzle: In a 3 X 3 matrix ((1 2 3)(4 5 6)(7 8 9)) the following numbers have to be checked: 9 single digit numbers 1...9;

40 2-digit numbers: row-wise 12, 21, 23, 32, 45, 54, 56, 65, 78, 87, 89, 98; column-wise 14, 41, 47, 74, 25, 52, 58, 85, 36, 63, 69, 96; diagonals 15, 51, 59, 95, 48, 84, 26, 62; anti-diagonals 35, 53, 57, 75, 24, 42, 68, 86;

16 3-digit numbers: 123, 321, 456, 654, 789, 987, 147, 741, 258, 852, 369, 963, 159, 951, 357, 753.

Cf. A109943 [Number of primes in the solution of the Gordon Lee puzzle].

Sequence in context: A043402 A044154 A044535 this_sequence A119285 A041494 A057689

Adjacent sequences: A034717 A034718 A034719 this_sequence A034721 A034722 A034723

nonn

Felice Russo (felice.russo(AT)katamail.com)

More terms from Hugo Pfoertner (hugo(AT)pfoertner.org), Jul 09 2005